History Forces in Oscillating Convective Flow Past a Fixed Particle

The determination of a consistent equation of motion for spherical particles in finite and infinitesimal Reynolds numbers is a classical problem in fluid mechanics. A number of keystone steps to develop and manipulate such Lagrangian equations of motion have been discussed in a steady stream of papers, starting at the end of the 19th century. The problem is of great complexity even for the limit of infinitesimal Reynolds numbers when both low and high frequency flows are considered. The complexity of the problem is evident when one considers that the surrounding fluid is continuously being deformed by the presence of the particle and therefore is continuously responding to particle accelerations according to its own inertialviscous balance. This intricate interaction translates into a striking feature: the so called history or Basset force. This force, which accounts for the effects of the local acceleration of the flow, is represented by an integro-differential operator. Coimbra and Rangel were the first to realize that the Basset force can ∗Graduate student, Department of Mechanical Engineering, 2540 Dole Street – Holmes Hall 302. †Assistant Professor, Department of Mechanical Engineering/SMA, Av. Rovisco Pais,1. ‡Associate Professor, Department of Mechanical Engineering, 2540 Dole Street – Holmes Hall 302. §Assistant Professor, Department of Mechanical Engineering, 2540 Dole Street – Holmes Hall 302. Copyright c © 2005 by H. T. C. Pedro, J. M. C. Pereira, M. H. Kobayashi and C. F. M. Coimbra. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission.